Question: Simplify the following expression: $ p = \dfrac{-2}{-3t - 8} - \dfrac{10}{3} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{-2}{-3t - 8} \times \dfrac{3}{3} = \dfrac{-6}{-9t - 24} $ Multiply the second expression by $\dfrac{-3t - 8}{-3t - 8}$ $ \dfrac{10}{3} \times \dfrac{-3t - 8}{-3t - 8} = \dfrac{-30t - 80}{-9t - 24} $ Therefore $ p = \dfrac{-6}{-9t - 24} - \dfrac{-30t - 80}{-9t - 24} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{-6 - (-30t - 80) }{-9t - 24} $ Distribute the negative sign: $p = \dfrac{-6 + 30t + 80}{-9t - 24}$ $p = \dfrac{30t + 74}{-9t - 24}$ Simplify the expression by dividing the numerator and denominator by -1: $p = \dfrac{-30t - 74}{9t + 24}$